Effective buoyancy and CAPE: Some implications for tropical cyclones

We review the widely used concepts of "buoyancy" and "convective available potential energy" (CAPE) in relation to deep convection in tropical cyclones and discuss their limitations. A fact easily forgotten in applying these concepts is that the buoyancy force of an air parcel, as often defined, is non-unique because it depends on the arbitrary definition of a reference density field. However, when calculating CAPE, the buoyancy of a lifted air parcel is related to the specific reference density field along a vertical column passing through that parcel. Both concepts can be generalized for a vortical flow and to slantwise ascent of a lifted air parcel in such a flow. In all cases, the air parcel is assumed to have infinitely small dimensions. In this article, we explore the consequences of generalizing buoyancy and CAPE for buoyant regions of finite size that perturb the pressure field in their immediate environment. Quantitative calculations of effective buoyancy, defined as the sum of the conventional buoyancy and the static vertical perturbation pressure gradient force induced by it, are shown for buoyant regions of finite width. For a judicious choice of reference density, the effective buoyancy per unit mass is essentially a unique force, independent of the reference density, but its distribution depends on the horizontal scale of the buoyant region. A corresponding concept of "effective CAPE" is introduced and its relevance to deep convection in tropical cyclones is discussed. The study is conceived as a first step to understanding the decreasing ability of inner-core deep convection in tropical cyclones to ventilate the mass of air converging in the frictional boundary layer as the vortex matures and decays.